Question

Hamming codeword : 011 1001 1101 0010 1110 01

By inverting one message bit in Hamming code word (to represent
a 1-bit error) and demonstrate how the recipient can use the
check bits to correct the inverted bit.

Answer 1

Solution Hamming Code Hamming code is Code is single error Correcting code of parity bits can be obtained from Number the formula gey P+m+l Where m= Num. of message bit pa parity bits for example Let message bit =m=4 apy, Prutl Hamming Code word 2 2 3 G Ineven parity Pp lam, P3 m2 m₂ my p> 1,3,5, 7, 9, 11, 13, 15, 17, 19, 2) Pa 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, Iz 4, 5, 6, 7, L2, 13, 14, 15, 10-23

For given Homming Cool word 4 0 2 3 2 2 2. 34 567 9 10 11 12 13 14 15 16 17 18 19 20 21 0101001 00 0 of w P R MP3 m m my Py ma ma ma mama 9wsw how my pro MM3 Ps P Pa Pa Pu Pd Parity Bits Message bit m. mama mums mom momg miomm, 2m, 3m, misma 00110 - O 0 (M s from 1 to o By Inverting message bita say

Checking Error By Inventing I message bit (M5 from 1 tool Mew or Received Hamming code 0 llloo Ilo o 1000 11100 2 3 4 5 6 12 13 14 14 16 17 18 19 to 2) 1 709 using odd Parity Es 16,17,18,19,20,21 → 11100) Eu 0,9,10, 11, 12,13,14,15 10010010 ► Ey=0 Ez a 4,5,6,7 2, 13, 14, 15,20,21 100/00/0, E30 2,3,6,7,10,11,14,15,18,19 – 1101011010, Egz! 1,3,5,7,9, 11, 13, 15, 17, 19, 21 → 0/0/0/00/01 Ei= 0 Error (lisation) E, E₂ E₃ Eu Es = olool Position So Correc code word will be obtain by bit on by I olllool11010010111ool which is some